1. Field of the Invention
This invention relates to high-Q micromechanical resonator devices and filters utilizing same.
2. Background Art
The following references are referenced herein:    [1] C. T.-C. Nguyen, “Vibrating RF MEMS for next Generation Wireless Applications,” PROCEEDINGS, 2004 IEEE CUSTOM INTEGRATED CIRCUITS CONF., Orlando, Fla., Oct. 3-6, 2004, pp. 257-264.    [2] A.A. Abidi, “Direct-conversion Radio Transceivers for Digital Comms,” IEEE J. SOLID-STATE CIRCUITS, vol. 30, No. 12, pp. 1399-1410, Dec. 1995.    [3] C. P. Yue and S.S. Wong, “On-Chip Spiral Inductors with Patterned Ground Shields for Si-Based RF IC's,” IEEE JOURNAL OF SOLID-STATE CIRCUITS, vol. 33, no. 5, pp. 743-752, May 1998.    [4] C. T.-C. Nguyen, “Transceiver Front-end Architectures Using Vibrating Micromechanical Signal Processors (Invited),” DIG. OF PAPERS , TOPICAL MEETING ON SILICON MONOLITHIC INTEGRATED CIRCUITS IN RF SYSTEMS , Sep. 12-14, 2001, pp. 23-32.    [5] C. T.-C. Nguyen, “Transceiver Front-end Architectures Using Vibrating Micromechanical Signal Processors,” CHAPTER IN RF TECHNOLOGIES FOR LOW POWER WIRELESS COMMUNICATIONS, Edited by G.I. Haddad, T. Itoh, and J. Harvey, pp. 411-461, New York: WILEY IEEE-PRESS, 2001.    [6] X. M. H. Huang, C.A. Zorman, M. Mehregany, M.L. Roukes, “Nanodevice Motion at Microwave Freqs,” NATURE, vol. 421, pg. 496, Jan. 30, 2003.    [7] J.R. Vig and Y. Kim, “Noise in Microelectromechanical System Resonators,” IEEE TRANS. UTRASON. FERROELEC. FREQ. CONTR., vol. 46, no. 6, pp. 1558-1565, Nov. 1999.    [8] J. Wang, Z. Ren, and C. T.-C. Nguyen, “Self-aligned 1.14-GHz Vibrating Radial-Mode Disk Resonators,” DIG. OF TECH PAPERS, TRANSDUCERS'03, Boston, Mass., Jun. 8-12, 2003, pp. 947-950.    [9] B. Bircumshaw, et al., “The Radial Bulk Annular Res.: Towards a 50 ΩMEMS Filter,” DIG. OF TECH PAPERS, TRANSDUCERS '03, Boston, Mass., Jun. 8-12, 2003, pp. 875-878.    [10] M. A. Abdelmoneum, M.U. Demirci, and C.T.-C. Nguyen, “Stemless Wine-glass-mode Disk Micromechanical Resonators,” PROCEEDINGS, 16TH INT. IEEE MEMS CONF., Kyoto, Japan, Jan. 19.-23, 2003, pp. 698-701.    [11] J. Wang, J.E. Butler, T. Feygelson, and C.T.-C. Nguyen, “1.51-GHz Polydiamond Micromechanical Disk Resonator with Impedancemismatched Isolating Support,” PROCEEDINGS, 17TH INT. IEEE MEMS CONF., Maastricht, The Netherlands, Jan. 25-29, 2004, pp. 641-644.    [12] J.R. Clark, A.-C. Wong, and C.T.-C. Nguyen, “Parallel-resonator Hf Micromechanical Bandpass Filters,” DIG. OF TECH. PAPERS, TRANSDUCERS '97, Chicago, Ill., Jun. 16-19, 1997, pp. 1161-1164.    [13] M. U. Demirci, M. A. Abdelmoneum, and C. T.-C. Nguyen, “Mechanically Corner-coupled Square Microresonator Array for Reduced Series Motional Resistance,” DIG. OF TECH. PAPERS, TRANSDUCERS '03, Boston, Mass., June 8-12, 2003, pp. 955-958.    [14] Antonio Iula, Nicola Lamberti, and Massimo Pappalardo, “A Model for the Theoretical Characterization of Thin Piezoceramic Rings,” IEEE TRANSACTIONS ON ULTRASONIC, FERROELECTRICS, AND FREQUENCY CONTROL, Vol. 43, No. 3, 1996, pp. 370-375.    [15] F. D. Bannon III, J. R. Clark, and C. T.-C. Nguyen, “High Frequency Micromechanical Filters,” IEEE J. SOLID-STATE CIRCUITS, vol. 35, no. 4, pp. 512-526, Apr. 2000.    [16] R. Navid, J. R. Clark, M. Demirci, and C. T.-C. Nguyen, “Third-order Intermodulation Distortion in Capacitively-Driven CC-beam Micromechanical Resonators,” TECHNICAL DIGEST, 14TH INT. IEEE MEMS CONF., Interlaken, Switzerland, Jan. 21-25, 2001, pp. 228-231.    [17] A.-C. Wong, H. Ding, and C. T.-C. Nguyen, “Micromechanical Mixer+Filters,” TECHNICAL DIGEST, IEEE INT. ELECTRON DEVICES MEETING, San Francisco, Calif., Dec. 6-9, 1998, pp. 471-474.Nomenclature    ri, ro, H Element dimensions (m).    r, θ, z Polar coordinates.    T Stress tenor (Pa).    cijE Elastic stiffness constant (Pa).    ρ Mass density (kg·m−3).    ur, Ur Displacement along the radial direction (m), displacement amplitude (m).    ω Angular frequency (rad·s−1).    t Time (s).    h Frequency parameter (rad·m−1).    VPhase wave velocity along the radial direction (m·s−1).    σ Poisson's ratio.    io, Io Output motional current (A), current amplitude (A).    q Electrical charge (C).    η Elecromechanical coupling coefficient (N/V).    X Mode displacement (m).    F Electrostatic force (N).    k Stiffness constant (N·M−1).    Q Quality factor.    Rx Motional resistance (Ω).    vi, Vi Input ac voltage (V), voltage amplitude (V).    C Time-varying capacitance (F).    d0 Electrode-to-resonator gap spacing (m).    A Electrode-to-resonator overlap area (m2).    ε0 Permittivity in vacuum (=8.854×10−12 F·m−1).Introduction
Today's wireless transceivers are generally designed under a mandate to minimize or eliminate the use of high-Q passives. The reasons for this are quite simple: cost and size. Specifically, the ceramic filters, SAW filters, quartz crystals, and now FBAR filters, capable of achieving the Q's from 500 to 10,000 needed for RF and IF bandpass filtering, and frequency generation functions, are all off-chip components that must interface with transistor circuits at the board-level, consuming excessive area and costing too much [1].
Pursuant to reducing the off-chip parts in modern cellular handsets, direct-conversion receiver architectures [2] have removed the IF filter, and integrated inductor technologies are removing some of the off-chip inductors used for bias and matching networks [3]. Although these methods can lower cost, they often do so at the expense of increased transistor circuit complexity and more stringent requirements on circuit performance, both of which degrade the robustness and power efficiency of the overall system. In addition, the removal of the IF filter does little to relax the requirements of future multi-band reconfigurable handsets that will likely require high-Q RF filters in even larger quantities.
Recent advances in vibrating RF micromechanical systems (“MEMS”) technology that have yielded on-chip resonators operating past GHz frequencies with Q's in excess of 10,000, may now not only provide an attractive solution to present day communication systems, but might also enable a paradigm-shift in transceiver design where the advantages of high-Q are emphasized, rather than suppressed [4][5]. In particular, like transistors, micromechanical elements can be used in large quantities without adding significant cost. This not only brings more robust superheterodyne architectures back into contention, but also encourages modifications to take advantage of a new abundance of low loss ultra-high-Q frequency shaping at GHz frequencies. For example, an RF channel select filter bank may now be possible, capable of eliminating not only out-of-band interferers, but also out-of-channel interferers, and in doing so, relaxing the dynamic range requirements of the LNA and mixer, and the phase noise requirements of the local oscillator, to the point of perhaps allowing complete transceiver implementations using very low cost transistor circuits.
A major impetus behind MEMS technology stems from the fact that mechanical mechanisms benefit from the same scaling-based advantages that have driven the integrated circuit revolution in recent decades. Specifically, small size leads to faster speed, lower power consumption, higher complexity, and lower cost. And it does so not only in the electrical domain, but in virtually all other domains, including and especially mechanical. Although many examples of this from all physical domains exist, vibrating RF MEMS resonators perhaps provide the most direct example of how small size leads to faster speed in the mechanical domain. Basically, further scaling down to nano-dimensions does indeed yield frequencies in excess of 1 GHz [6]. However, as with nanoelectronics in the electrical domain, there are issues in the mechanical domain that might hinder the use of nanomechanical vibrating resonators for today's communication purposes. In particular, excessive scaling may lead to “scaling-induced limitations,” such as adsorption-desorption noise [7], temperature fluctuation noise, and insufficient power handling, with the last of these perhaps being the most serious for present day applications. As with nanoelectronics, the power handling issue with nanomechanical resonators really boils down to an impedance matching problem. In brief, nanostructures would rather operate at higher impedance levels than macroscopic counterparts, and in order to interface the nano with the macro (e.g., the antenna), impedance matching strategies like massive arraying of nanostructures to add their responses might be required.
Fortunately, massive-scale arraying isn't really needed, at least not for the frequency range used by present day commercial wireless standards. In particular, GHz frequencies can be attained mechanically without the need for nano-scale dimensions, and thus, without its associated power handling issues, by merely using ring resonator geometry that operate in modes more amenable to higher frequency.
Wireless communication receivers could be greatly simplified if communication channels (rather than bands of channels) could be selected right at RF, immediately after the antenna, with out-of-channel noise and interferers removed before the received signal reaches any transistor circuits. With such an RF channel-selection capability, a wireless receiver might dispense with multi-stage down-conversion circuits, and instead, utilize a direct sub-sampling A/D converter right at the front end. Unfortunately, RF channel-selection is extremely difficult, because it requires at least 0.1% bandwidth selectivity, which, in turn, requires filters using resonators with Q's >10,000 to maintain acceptable insertion loss (below 1 dB). Although on-chip MEMS-based vibrating resonators have very recently reached frequencies past 1 GHz [8], they have so far not done so with Q's as high as 10,000. Even off-chip resonators in use today, such as SAW's or FBAR's, exhibit Q's about an order of magnitude lower than the needed 10,000.